Note from Traci Monday night -- See "Deductive Vignettes" Wiki page for link to revised Vignettes Word doc.
A mathematical induction story: While doing her homework one night, Sahara found herself factoring a lot of numbers. She noticed that every time she factored an odd number, she got only odd factors. She saw that 17 = 17(1 ), 25 = 5(5), 51 = 3(17). After she finished her homework, she tried about 20 more numbers that she hadn’t done in her homework, and she found that all of her odd numbers had only odd factors. Sahara smiled and said to herself, “Odd numbers have only odd factors.”
Stacey
Another induction story:
Kimo substitutes the numbers 1, 2, 3, 4, 5, 6, and 7, for n in the expression n^2 + n + 41.
His results are all prime numbers: 43, 47, 53, 63, 71, 83, and 97.
He makes a conclusion: If I substitute any positive integer for n, then the result will be prime.
Bill
Given the following numbers, what number do you think comes next?
1, 4, , 16, . . .
(Marty) Taken together:
1) One the first day of a flu outbreak, two people were sick with the flu. On the second day, four people were sick with the flu. So, on the third day six people will be sick with the flu because it seems that the number increased from the first to second day.
2) On the first day of a flu outbreak, two people were sick with the flu. On the second day, four people were sick with the flu. So, on the third day eight people will be sick with the flu because it seems that the number doubled from the first to second day.
Isaiah saw a webpage that showed the official portraits (pictures) of all the Presidents of the United States. He did some research and found out that an official portrait is created around the time each new president takes office. Looking at the pictures, Isaiah thought that all of the presidents looked older than Isaiah's dad, who was 38. So he decided there must be a law requiring a person to be at least 35 to be elected president.
Note from Traci Monday night -- See "Deductive Vignettes" Wiki page for link to revised Vignettes Word doc.
A mathematical induction story:
While doing her homework one night, Sahara found herself factoring a lot of numbers. She noticed that every time she factored an odd number, she got only odd factors. She saw that 17 = 17(1 ), 25 = 5(5), 51 = 3(17). After she finished her homework, she tried about 20 more numbers that she hadn’t done in her homework, and she found that all of her odd numbers had only odd factors. Sahara smiled and said to herself, “Odd numbers have only odd factors.”
Stacey
Another induction story:
Kimo substitutes the numbers 1, 2, 3, 4, 5, 6, and 7, for n in the expression n^2 + n + 41.
His results are all prime numbers: 43, 47, 53, 63, 71, 83, and 97.
He makes a conclusion: If I substitute any positive integer for n, then the result will be prime.
Bill
Given the following numbers, what number do you think comes next?
1, 4, , 16, . . .
(Marty) Taken together:
1) One the first day of a flu outbreak, two people were sick with the flu. On the second day, four people were sick with the flu. So, on the third day six people will be sick with the flu because it seems that the number increased from the first to second day.
2) On the first day of a flu outbreak, two people were sick with the flu. On the second day, four people were sick with the flu. So, on the third day eight people will be sick with the flu because it seems that the number doubled from the first to second day.
Isaiah saw a webpage that showed the official portraits (pictures) of all the Presidents of the United States. He did some research and found out that an official portrait is created around the time each new president takes office. Looking at the pictures, Isaiah thought that all of the presidents looked older than Isaiah's dad, who was 38. So he decided there must be a law requiring a person to be at least 35 to be elected president.